Sample-Path Analysis of Queueing Systems

Sample-Path Analysis of Queueing Systems by Muhammad El-Taha, Shaler Stidham Jr.

Sample-Path Analysis of Queueing Systems uses a deterministic (sample-path) approach to analyze stochastic systems, primarily queueing systems and more general input-output systems. Among other topics of interest it deals with establishing fundamental relations between asymptotic frequencies and ave...

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Bibliographic Details
Main Authors: El-Taha, Muhammad (Author), Stidham Jr., Shaler (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: New York, NY : Springer US : Imprint: Springer, 1999.
Edition:1st ed. 1999.
Series:International Series in Operations Research & Management Science, 11
Springer eBook Collection.
Subjects:
Operations research.
Decision making.
Probabilities.
Mathematical optimization.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
Table of Contents:
  • 1. Introduction and Overview
  • 1.1 Introduction
  • 1.2 Elementary Properties of Point Processes: Y = ?X
  • 1.3 Little’s Formula: L = ?W
  • 1.4 Stability and Imbedded Properties of Input-Output Systems
  • 1.5 Busy-Period Analysis
  • 1.6 Conditional Properties of Queues
  • 1.7 Comments and References
  • 2. Background and Fundamental Results
  • 2.1 Introduction
  • 2.2 Background on Point Processes: Y = ?X
  • 2.3 Cumulative Processes
  • 2.4 Rate-Conservation Law
  • 2.5 Fundamental Lemma of Maxima
  • 2.6 Time-Averages and Asymptotic Frequency Distributions
  • 2.7 Comments and References
  • 3. Processes with General State Space
  • 3.1 Introduction
  • 3.2 Relations between Frequencies for a Process with an Imbedded Point Process
  • 3.3 Applications to the G/G/1 Queue
  • 3.4 Relations between Frequencies for a Process with an Imbedded Cumulative Process (Fluid Model)
  • 3.5 Martingale ASTA
  • 3.6 Comments and References
  • 4. Processes with Countable State Space
  • 4.1 Introduction
  • 4.2 Basic Relations
  • 4.3 Networks of Queues: The Arrival Theorem
  • 4.4 One-Dimensional Input-Output Systems
  • 4.5 Applications to Stochastic Models
  • 4.6 Relation to Operational Analysis
  • 4.7 Comments and References
  • 5. Sample-Path Stability
  • 5.1 Introduction
  • 5.2 Characterization of Stability
  • 5.3 Rate Stability for Multiserver Models
  • 5.4 Rate Stability for Single-Server Models
  • 5.5 ?-Rate Stability
  • 5.6 Comments and References
  • 6. Little’s Formula and Extensions
  • 6.1 Introduction
  • 6.2 Little’s Formula: L = ?W
  • 6.3 Little’s Formula for Stable Queues
  • 6.4 Generalization of Little’s Formula: H = ?G
  • 6.5 Fluid Version of Little’s Formula
  • 6.6 Fluid Version of H = ?G 190 6.6.1 Necessary and Sufficient Conditions
  • 6.7 Generalization of H = ?G
  • 6.8 Applications to Stochastic Models
  • 6.9 Comments and References
  • 7. Insensitivity of Queueing Networks
  • 7.1 Introduction
  • 7.2 Preliminary Result
  • 7.3 Definitions and Assumptions
  • 7.4 Infinite Server Model
  • 7.5 Erlang Loss Model
  • 7.6 Round Robin Model
  • 7.7 Comments and References
  • 8. Sample-Path Approach to Palm Calculus
  • 8.1 Introduction
  • 8.2 Two Basic Results
  • 8.3 Extended Results
  • 8.4 Relation to Stochastic Models
  • 8.5 Comments and References
  • Appendices
  • References.

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